of the quantum torus algebra spanned by formal variables \(\mathcal {X}_\gamma \)  satisfying
\(\mathcal {X}_\gamma \, \mathcal {X}_{\gamma ^{\prime }} =(-y)^{\langle \gamma ,\gamma ^{\prime }\rangle } \mathcal {X}_{\gamma +\gamma ^{\prime }}\) .
The set \(\mathcal {D}_\psi \)  of all active rays \(\mathcal {R}_\psi (\gamma )\)  equipped with
\(\mathcal {U}_Z(\gamma )\)  then forms a consistent scattering diagram, which informally means that the product of the
automorphisms \(\mathcal {U}_Z(\gamma )\)  around each codimension-two intersection must equal one. This property uniquely
specifies the invariants \(\bar{\Omega }_Z(\gamma )\)  on outgoingWe postpone the definition of incoming and outgoing rays to §REF .
For the present discussion, it suffices to orient the restriction of the rays along a transverse
plane in the vicinity of a codimension-two intersection, according to the gradient of the central
charge \(|Z(\gamma )|\) .
rays in terms of those on incoming rays.
In the context of quivers with potential, one can further restrict the scattering diagram from
the space \(({H}_B)^{n}\)  of Bridgeland stability conditions (where \({H}_B\)  is the upper
half-plane \(\lbrace  z\in {C}: \Im z> 0 \ \mbox{or}\ (\Im z=0 \ \mbox{and}\ \Re z<0) \rbrace \)  and
\(n\)  denotes the number of nodes in the quiver)
to the
space \({R}^n\)  of King stability conditions, such that \(\mathcal {D}_\psi \)  becomes a complex of convex rational polyhedral cones [1]}.
